We use the average negative log-likelihood (a.k.a log-loss) measured on the test set as our primary metric of performance. In Table REF  we summarize the results of NGBoost and the suite of competitors that were evaluated in  [1]} and then add in the results for PRESTO (structured variant). For brevity, we report the values only for NGBoost and the method that gave the best value for that particular dataset. We will briefly summarize the competing methods here - for full details see  [1]} and the associated papers. The Concrete Dropout method ([3]}) fits a neural network and uses a continuous relaxation to tune the dropout probability. Deep Ensembles ([4]}) fit multiple neural networks and then approximate a Gaussian mixture to obtain a probability distribution. The Gaussian Processes method ([5]}) used a relevance detection kernel optimized by gradient descent and employing a variational inference technique from [6]}. The DistForest method ([7]}) used forests of 200 trees to estimate the parameters of a Normal distribution.
